2021 Vol. 42, No. 10

Display Method:
A Special Issue on Applied Mathematics and Mechanics Related to Cellular Mechanical Microenvironment
2021, 42(10): 1-2.
Abstract(190) PDF(77)
Research Advances in Cell Durotaxis
YANG Yuehua, JIANG Hongyuan
2021, 42(10): 999-1007. doi: 10.21656/1000-0887.420265
Abstract(415) PDF(93)
The cellular mechanical microenvironment can regulate many cellular physiological functions. In particular, cells can migrate directionally under external cue gradients from their mechanical microenvironment. These directed migrations play critical roles in wound healing, cancer cell metastasis, and tissue morphology development. So far, directional cell migration mostly includes: the directional migration under chemical gradients (chemotaxis), the directional migration under adhesion gradients (haptotaxis), and the directional migration under mechanical gradients (durotaxis). Although the basic mechanisms of chemotaxis and haptotaxis are well characterized, the mechanism of durotaxis remains unclear. In this review, we describe the experimental and theoretical advances in the study of cell durotaxis, analyze the connections and differences among different studies, discuss the potential mechanical mechanism of cell durotaxis, and put forward the remaining problems and possible future research directions.
Stretching a Polymer Chain in a Confined Space
LI Kai, YE Tianyu, WANG Jizeng
2021, 42(10): 1008-1023. doi: 10.21656/1000-0887.420279
Abstract(316) PDF(68)
The quantitative characterization of micromechanical properties of polymer biomaterials and the development of advanced biological micro-/nano- technology and devices need to quantitatively analyze the statistical thermodynamic properties and behaviors of polymer chains such as biological macromolecules in complex microenvironment. In the process of achieving this goal, the cross research of continuum mechanics and statistical thermodynamics plays a very important role. Aiming at the mechanics problems in this field, starting from the force stretching of DNA molecules, and by introducing several theoretical models describing the statistical thermodynamic properties of polymer chains, it is pointed out that the wormlike chain model has more significant advantages in describing the relationship between force and configuration change of semi-flexible polymer chains than other ideal random chain models, so that the qualitative and quantitative understanding of the statistical thermodynamic properties and behavior of polymers in complex microenvironment has become largely dependent on the relevant research progresses based on the wormlike chain model. Based on this fact, by reviewing the research on the influence of geometric constraints on the random conformation distribution of polymer chains, the research on the statistical thermodynamic model of polymer chains under the simultaneous action of tension and constraints, and the simulation research on the statistical physical properties of polymer chains based on high-performance computers, the latest progress and challenging problems in the research of statistical thermodynamic properties and behavior of worm chains under different constraints and stress microenvironments are summarized. Finally, through summary and analysis, it is pointed out that the study of statistical thermodynamics of worm chain in complex microenvironment is an important basis for understanding life phenomena from the molecular and cell scale, developing advanced micro- and nano- technology and constructing the constitutive relationship of soft matter. At present, it has become a very challenging frontier topic in the interdisciplinary of mechanics.
Mechanical Modeling and Analyses of Cytoskeleton and Extracellular Matrix
GONG Bo, LIN Ji, WANG Yanzhong, QIAN Jin
2021, 42(10): 1024-1044. doi: 10.21656/1000-0887.420302
Abstract(343) PDF(76)
The cells and biological tissues need to adapt the complex physiological and mechanical environment in human body. They must withstand the mechanical loads from external environment, and equally important, they often actively produce forces to change their architecture and shape during physiological processes such as tissue growth and repair. The mechanical properties of cells are mainly determined by cytoskeleton, and the stiffness of biological tissues is greatly affected by extracellular matrix. Microscopically, cytoskeleton and extracellular matrix are intricate, heterogeneous 3D networks of crosslinked biopolymers. Early studies mainly focused on explaining the universal features such as the nonlinear response and strain stiffening of these biopolymer networks by constructing various network models. In recent years, with the simultaneous progress in experimental methods, theoretical models and computational techniques, more intriguing mechanical behaviors and underlying mechanisms of these living matters have been revealed. In this review, we online some of the major advances in modeling and analyzing cytoskeleton and extracellular matrix, including the dynamic crosslinking, active materials originated from mechanochemical coupling of biopolymers, plasticity/fracture of crosslinked networks, and self-adaption triggered by mechanical training. These modeling and analyses may help to quantify the complex behaviors of cells and tissues, deepen our understanding of the underlying mechanobiological mechanisms, and provide guidance for synthetic biological materials and tissue engineering.
Mechanics of Low-Temperature Phase Transition in Liquid-Filled Elastic Capillary Tube
TAO Ze, LI Moxiao, TI Fei, LIU Yonggang, LIU Shaobao, LU Tianjian
2021, 42(10): 1045-1061. doi: 10.21656/1000-0887.420301
Abstract(419) PDF(65)
Liquid-filled elastic capillaries are a kind of standard component in life body (e.g., capillary blood vessel and plant vessel) and engineering fields (e.g., MEMS microchannel resonators and heat pipes). Under sufficiently low-temperature, the liquid in a capillary tube will undergo a phase transition and exhibit a frozen-heave effect, which may cause deformation, damage, and even fracture of the tube wall. In this study, we established the governing equation of an elastic capillary tube, with temperature gradient, interfacial tension, and frozen-heave effect accounted for, and solved the equation for stresses developed in the tube wall during freezing. It is demonstrated that stress distribution in tube wall is influenced by the thermoelastocapillary number and the freezeoelastocapillary number, both dependent upon wall thickness. Results obtained in this study are not only helpful for understanding the prevention of frozen-heave failure, but also provide theoretical guidance for tailoring the freezing resistance of microfluidic devices used in MEMS.
Three-Dimensional Collective Cell Dynamics Model Basedon Elastic Shells
YU Pengyu, XU Kun, CHEN Pengcheng, LI Bo
2021, 42(10): 1062-1073. doi: 10.21656/1000-0887.420264
Abstract(404) PDF(86)
Collective cell migration occurs in various physiological and pathological processes such as embryonic development, wound healing and tumor invasion. Studies on collective dynamics are crucial for understanding the mechanism underlying collective cell migration and its related biological processes. Here, we propose a three-dimensional (3D) multicellular model based on elastically deformable shells. The equation of motion on the vertices of the cell was established. A 3D collective cell dynamics theory that involves cell deformations and intercellular contact and adhesion is established, and the corresponding numerical algorithm is developed. Based on the developed dynamic model, the rotation of collective cell confined in a spherical lumen is simulated. Our simulations reproduce the experimental observation. Further, we analyze the influence of cell polarity, cell deformations, and intercellular interactions on the 3D dynamics of collective cells.
A Molecular Clutch Model of Cellular Adhesion on Viscoelastic Substrate
2021, 42(10): 1074-1080. doi: 10.21656/1000-0887.420259
Abstract(352) PDF(58)
The viscoelastic nature of the microenvironment of a cell is critical to cell mechanobiology, and modulates the mechanical feedback between cells and extracellular matrix. However, the mechanisms underlying the ways that cells actively sense and respond to a viscoelastic microenvironment remain elusive. We therefore developed a molecular clutch model of cell traction to predict the effects of substrate viscoelasticity on the dynamics of focal adhesions connecting the intracellular actin cytoskeleton to a viscoelastic substrate. The model predicts that certain levels of viscoelastic damping can increase cell tractions on relatively compliant substrates, and that this damping reduces cell tractions on relatively stiff substrates. The model predictions are qualitatively consistent well with reported experimental observations. The model offers physical insights into the role of substrate viscoelasticity on cell tractions and cell spreading.
Molecular Simulation Study on the Interaction Between SARS-CoV-2 Main Protease and the Antiviral Inhibitors
WU Xuwei, LI Xingyu, LI Hua, LI Zhenhai, CHEN Wei, LI Dechang
2021, 42(10): 1081-1090. doi: 10.21656/1000-0887.420280
Abstract(566) PDF(55)
In this study, we studied the interactions between the inhibitors and the main protease (Mpro) of SARS-CoV-2, to understand how the inhibitors influence the dynamics of Mpro of SARS-CoV-2. Firstly, we applied molecular docking to obtain the binding complex of the inhibitors and the main protease, and the binding affinities. The classical molecular dynamics simulations showed that all of the tested inhibitors cannot inhibit the dynamics of Mpro’s active pocket. The replica-exchange molecular dynamics simulations showed that the inhibitors influence the shape of the active pocket of Mpro. With the formation of hydrogen bonds between the inhibitor and different sites of the active pocket, the inhibitors affect the length and width of the pocket. Our study indicated that the drug design of Mpro should fully consider the importance of the hydrogen network between the potential inhibitor and the active pocket.
Theoretical and Simulation Studies on the Effect of Molecular Stiffness on Binding Kinetics of Membrane-Anchored Receptors And Ligands
ZHONG Chuhan, XU Guangkui
2021, 42(10): 1091-1102. doi: 10.21656/1000-0887.420262
Abstract(543) PDF(64)
Cell adhesion plays an important role in most biological processes in human body. Cell adhesion is mainly determined by the binding kinetics of specific molecules (called receptors and ligands) anchored on the cell membrane. Although it is known that the binding relation of specific molecules is affected by various factors as external forces and cell membrane fluctuations, it is still unclear how the molecular stiffness affects the binding relation between the membrane-anchored receptors and ligands. Recent studies on the strong infectivity of the coronavirus have shown the importance of specific molecular stiffness to the adhesion between virus and cells. Here, we develop a coarse-grained model of biomembrane adhesion, and use molecular simulation and theoretical analysis to reveal the role of molecular stiffness in adhesion. The results show that there is always an optimal membrane and an optimal molecular stiffness value, and the adhesion molecular affinity and binding kinetic parameters reach the maximum. This study can not only deepen the understanding of cell adhesion, but also help guide drug design and vaccine development.